PTC Thermistor

Positive temperature coefficient (PTC) thermistor

Libraries:
Simscape / Electrical / Sensors & Transducers

Description

The PTC thermistor block models a positive temperature coefficient (PTC) thermistor. To model a switching PTC thermistor or a resistance temperature detector (RTD), use this block. To model a non-switching linear PTC thermistor, use the Thermal Resistor block.

The thermal behavior of the block uses the equation

$Q = K_{d} t_{c} \frac{d T}{d t} - I^{2} R,$

where:

Q is the net heat flow into the A port.
K_d is the Dissipation factor parameter value.
t_c is the Thermal time constant parameter value.
dT/dt is the rate of change of temperature with respect to time.
I is the current.
R is the resistance.

Note

You must not connect the PTC Thermistor block to an ideal current source. This arrangement creates a positive feedback loop that results in thermal runaway because:

Increasing the temperature increases the resistance
Increasing the resistance with an ideal current source increases the voltage
Increasing the voltage increases the dissipated power
Increasing the dissipated power increases the temperature, which closes the loop

Temperature Operating Limits

Since R2024a

If you set the Thermistor parameterization type parameter to Switching Thermistor, you can choose whether to specify the range of operating temperatures by using the Enable temperature operating limits parameter. If you set the Thermistor parameterization type parameter to RTD (Callendar - Van Dusen coefficients), you must specify the range of operating temperatures.

Specify the lower and upper temperature operating limits by setting the Minimum operating temperature and Maximum operating temperature parameters, respectively. Find these values on a datasheet. If the temperature falls outside of the operating limits:

If you set Reporting if operating limits exceeded to Warn, Simulink^® displays a warning and the simulation continues.
If you set Reporting if operating limits exceeded to Error, Simulink displays an error and terminates the simulation.

Switching Thermistor

To model a switching PTC thermistor, set the Thermistor parameterization type parameter to Switching Thermistor. This type of thermistor has a decreasing resistance with increasing temperature up to the Curie temperature T_c. Above the Curie temperature, the resistance increases rapidly with increasing temperature. The region to the right of T_c in this figure is called the PTC regime.

This equation defines the resistance R at temperature T,

$R = {\begin{array}{r} R_{0} e^{α_{0} (T - T_{0})} for T \leq T_{c} \\ R_{1} e^{α_{1} (T - T_{1})} for T \geq T_{c} \end{array}$

$T_{c} = \frac{\log (R_{1}) - \log (R_{0}) + α_{0} T_{0} - α_{1} T_{1}}{α_{0} - α_{1}}$

where:

R₀ is the resistance at the nominal temperature.
R₁ is the resistance at the reference temperature.
α₀ is the temperature coefficient at the nominal temperature.
α₁ is the temperature coefficient at the reference temperature.
T₀ is the nominal temperature at which you quote the nominal resistance, usually room temperature. T₀ must be less than the Curie temperature.
T₁ is the reference temperature at which you quote the reference resistance. T₁ must be in the PTC regime.

Resistance Temperature Detector

Since R2024a

To model an RTD, set the Thermistor parameterization type to RTD (Callendar - Van Dusen coefficients). The Callendar–Van Dusen equation defines the resistance R at temperature T. This equation uses T measured in degC,

$R = {\begin{array}{r} R_{0} (1 + A T + B T^{2} + C (T - 100) T^{3} ) for T \leq 0 \\ R_{0} (1 + A T + B T^{2}) for T \geq 0 \end{array}$

where:

R₀ is the resistance at the nominal temperature of 0 degC.
A, B, and C are the Callendar–Van Dusen coefficients.

You can find these coefficients on a datasheet. The default parameter values that the block uses are typical for platinum RTDs. The R-T characteristic is approximately linear within the range of operating temperatures so choose values of B and C that are several orders of magnitude smaller than A.

Simulink displays a warning if the resistance does not increase monotonically over the range of operating temperatures. If you set the Reporting if operating limits exceeded parameter to Warn and the temperature falls outside of the operating range, the block uses linear extrapolation to calculate the resistance with respect to temperature.

Variables

To set the priority and initial target values for the block variables before simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Use nominal values to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources. One of these sources is the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

Ports

Conserving

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A — Thermal mass
thermal

Thermal conserving port associated with the thermal mass.

+ — Positive terminal
electrical

Electrical conserving port associated with the positive terminal.

- — Negative terminal
electrical

Electrical conserving port associated with the negative terminal.

Parameters

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Electrical

Thermistor parameterization type — Thermistor type
`Switching Thermistor` (default) | `RTD (Callendar - Van Dusen coefficients)`

Since R2024a

Thermistor type. This parameter determines the equations that the block uses to calculate the resistance as a function of temperature. Choose one of these options:

Switching Thermistor — Model a switching thermistor. Specify the temperature coefficient and electrical resistance at a nominal temperature and a reference temperature.
RTD (Callendar - Van Dusen coefficients) — Model a resistance temperature detector. Specify the Callendar–Van Dusen coefficients and the nominal resistance at 0 degC.

Nominal resistance R0 at T0 — Resistance at nominal temperature
`1000` `Ohm` (default) | positive scalar

Resistance at the nominal temperature. Datasheets often list the nominal resistance at 25 degrees Celsius as R25.

Dependencies

To enable this parameter, set Thermistor parameterization type to Switching Thermistor.

Temperature coefficient alpha0 at T0 — Temperature coefficient at nominal temperature
`-0.01` `1/K` (default) | negative scalar

Temperature coefficient at the nominal temperature.

Dependencies

To enable this parameter, set Thermistor parameterization type to Switching Thermistor.

Nominal temperature T0 — Nominal temperature
`298.15` `K` (default) | positive scalar

Temperature at which you quote the nominal resistance.

Dependencies

To enable this parameter, set Thermistor parameterization type to Switching Thermistor.

Reference resistance R1 at T1 — Resistance at reference temperature
`10000` `Ohm` (default) | positive scalar

Resistance at the reference temperature.

Dependencies

To enable this parameter, set Thermistor parameterization type to Switching Thermistor.

Temperature coefficient alpha1 at T1 — Temperature coefficient at reference temperature
`1` `1/K` (default) | positive scalar

Temperature coefficient at the reference temperature.

Reference temperature T1 — Reference temperature
`398.15` `K` (default) | scalar

Temperature at which you quote the reference resistance. This temperature must be in the PTC regime.

Dependencies

To enable this parameter, set Thermistor parameterization type to Switching Thermistor.

Nominal resistance R0 at 0 degC — Resistance at nominal temperature
`100` `Ohm` (default) | positive scalar

Since R2024a

Resistance at the nominal temperature of 0 degrees Celsius.

Dependencies

To enable this parameter, set Thermistor parameterization type to RTD (Callendar - Van Dusen coefficients).

A Coefficient [degC^-1] — `A` coefficient
`3.9083e-3` (default) | positive scalar

Since R2024a

A coefficient in the Callendar–Van Dusen equation. The default value is typical for platinum RTDs.

Dependencies

To enable this parameter, set Thermistor parameterization type to RTD (Callendar - Van Dusen coefficients).

B Coefficient [degC^-2] — `B` coefficient
`-5.775e-7` (default) | scalar

Since R2024a

B coefficient in the Callendar–Van Dusen equation. The default value is typical for platinum RTDs.

Dependencies

To enable this parameter, set Thermistor parameterization type to RTD (Callendar - Van Dusen coefficients).

C Coefficient [degC^-4] — `C` coefficient
`-4.183e-12` (default) | scalar

Since R2024a

C coefficient in the Callendar–Van Dusen equation. The default value is typical for platinum RTDs.

Dependencies

To enable this parameter, set Thermistor parameterization type to RTD (Callendar - Van Dusen coefficients).

Temperature Operating Limits

Enable temperature operating limits — Option to specify temperature operating limits
`No` (default) | `Yes`

Since R2024a

Option to specify the operating limits for the temperature.

Dependencies

To enable this parameter, set Thermistor parameterization type to Switching Thermistor.

Reporting if operating limits exceeded — Reporting if temperature falls outside operating range
`Warn` (default) | `Error`

Since R2024a

Reporting if the temperature falls outside of the operating limits. Choose one of these options:

Warn — Simulink displays a warning and the simulation continues.
Error — Simulink displays an error and terminates the simulation.

Dependencies

To enable this parameter, choose one of these options:

Set Thermistor parameterization type to Switching Thermistor and Enable temperature operating limits to Yes.
Set Thermistor parameterization type to RTD (Callendar - Van Dusen coefficients).

Minimum operating temperature — Lower limit of operating temperature range
`223.15` `K` (default) | scalar

Since R2024a

Lower limit of the operating temperature range.

Dependencies

To enable this parameter, choose one of these options:

Set Thermistor parameterization type to Switching Thermistor and Enable temperature operating limits to Yes.
Set Thermistor parameterization type to RTD (Callendar - Van Dusen coefficients).

Maximum operating temperature — Upper limit of operating temperature range
`428.15` `K` (default) | scalar

Since R2024a

Upper limit of the operating temperature range.

Dependencies

To enable this parameter, choose one of these options:

Set Thermistor parameterization type to Switching Thermistor and Enable temperature operating limits to Yes.
Set Thermistor parameterization type to RTD (Callendar - Van Dusen coefficients).

Thermal

Thermal time constant — Thermal time constant
`5.0` `s` (default) | positive scalar

Time it takes for the thermistor temperature to change by 63% of the final temperature change when there is a step change in the ambient temperature.

Dissipation factor — Dissipation factor
`0.75e-3` `W/K` (default) | positive scalar

Thermal power needed to raise the thermistor temperature by 1 K.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2012b

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R2024a: Model resistance temperature detector

You can now model a resistance temperature detector (RTD). The block uses the Callendar–Van Dusen equation to calculate the resistance as a function of temperature. To enable this option, set the Thermistor parameterization type parameter to RTD (Callendar – Van Dusen coefficients).

If you model an RTD, you must specify operating temperature limits. If you model a switching-type thermistor, you can now choose to specify the operating temperature limits.

R2024a: Model self-heating

The PTC Thermistor block now models self-heating. This equation describes the thermal behavior of the block:

$Q = K_{d} t_{c} \frac{d T}{d t} - I^{2} R .$

For a definition of each of the variables, see Description.

Before 2024a, the equation that the block uses does not include the IR² term. This change improves modeling accuracy without slowing down the simulation.

As a result of this change, you must not connect the block to an ideal current source because this arrangement creates a positive feedback loop that results in thermal runaway.

PTC Thermistor

Description

Temperature Operating Limits

Switching Thermistor

Resistance Temperature Detector

Variables

Ports

Conserving

A — Thermal mass thermal

+ — Positive terminal electrical

- — Negative terminal electrical

Parameters

Electrical

Thermistor parameterization type — Thermistor type Switching Thermistor (default) | RTD (Callendar - Van Dusen coefficients)

Nominal resistance R0 at T0 — Resistance at nominal temperature 1000 Ohm (default) | positive scalar

Dependencies

Temperature coefficient alpha0 at T0 — Temperature coefficient at nominal temperature -0.01 1/K (default) | negative scalar

Dependencies

Nominal temperature T0 — Nominal temperature 298.15 K (default) | positive scalar

Dependencies

Reference resistance R1 at T1 — Resistance at reference temperature 10000 Ohm (default) | positive scalar

Dependencies

Temperature coefficient alpha1 at T1 — Temperature coefficient at reference temperature 1 1/K (default) | positive scalar

Reference temperature T1 — Reference temperature 398.15 K (default) | scalar

Dependencies

Nominal resistance R0 at 0 degC — Resistance at nominal temperature 100 Ohm (default) | positive scalar

Dependencies

A Coefficient [degC^-1] — A coefficient 3.9083e-3 (default) | positive scalar

Dependencies

B Coefficient [degC^-2] — B coefficient -5.775e-7 (default) | scalar

Dependencies

C Coefficient [degC^-4] — C coefficient -4.183e-12 (default) | scalar

Dependencies

Temperature Operating Limits

Enable temperature operating limits — Option to specify temperature operating limits No (default) | Yes

Dependencies

Reporting if operating limits exceeded — Reporting if temperature falls outside operating range Warn (default) | Error

Dependencies

Minimum operating temperature — Lower limit of operating temperature range 223.15 K (default) | scalar

Dependencies

Maximum operating temperature — Upper limit of operating temperature range 428.15 K (default) | scalar

Dependencies

Thermal

Thermal time constant — Thermal time constant 5.0 s (default) | positive scalar

Dissipation factor — Dissipation factor 0.75e-3 W/K (default) | positive scalar

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

R2024a: Model resistance temperature detector

R2024a: Model self-heating

See Also

A — Thermal mass
thermal

+ — Positive terminal
electrical

- — Negative terminal
electrical

Thermistor parameterization type — Thermistor type
`Switching Thermistor` (default) | `RTD (Callendar - Van Dusen coefficients)`

Nominal resistance R0 at T0 — Resistance at nominal temperature
`1000` `Ohm` (default) | positive scalar

Temperature coefficient alpha0 at T0 — Temperature coefficient at nominal temperature
`-0.01` `1/K` (default) | negative scalar

Nominal temperature T0 — Nominal temperature
`298.15` `K` (default) | positive scalar

Reference resistance R1 at T1 — Resistance at reference temperature
`10000` `Ohm` (default) | positive scalar

Temperature coefficient alpha1 at T1 — Temperature coefficient at reference temperature
`1` `1/K` (default) | positive scalar

Reference temperature T1 — Reference temperature
`398.15` `K` (default) | scalar

Nominal resistance R0 at 0 degC — Resistance at nominal temperature
`100` `Ohm` (default) | positive scalar

A Coefficient [degC^-1] — `A` coefficient
`3.9083e-3` (default) | positive scalar

B Coefficient [degC^-2] — `B` coefficient
`-5.775e-7` (default) | scalar

C Coefficient [degC^-4] — `C` coefficient
`-4.183e-12` (default) | scalar

Enable temperature operating limits — Option to specify temperature operating limits
`No` (default) | `Yes`

Reporting if operating limits exceeded — Reporting if temperature falls outside operating range
`Warn` (default) | `Error`

Minimum operating temperature — Lower limit of operating temperature range
`223.15` `K` (default) | scalar

Maximum operating temperature — Upper limit of operating temperature range
`428.15` `K` (default) | scalar

Thermal time constant — Thermal time constant
`5.0` `s` (default) | positive scalar

Dissipation factor — Dissipation factor
`0.75e-3` `W/K` (default) | positive scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.